Exploring Quantum Annealing Architectures: A Spin Glass Perspective

TL;DR

This study investigates the spin-glass phase transitions in various Ising models relevant for quantum annealers, revealing that certain quasi-two-dimensional graphs exhibit only a zero-temperature spin-glass state, impacting their computational complexity.

Contribution

It provides the first detailed analysis of spin-glass transitions in quasi-two-dimensional graphs used in quantum annealers, highlighting their potential complexity and limitations for classical algorithms.

Findings

Random lattices show a spin-glass phase at finite temperature.

Quasi-two-dimensional graphs exhibit only zero-temperature spin-glass states.

Computational cost increases sharply near pseudo-critical temperatures.

Abstract

We study the spin-glass transition in several Ising models of relevance for quantum annealers. We extract the spin-glass critical temperature by extrapolating the pseudo-critical properties obtained with Replica-Exchange Monte-Carlo for finite-size systems. We find a spin-glass phase for some random lattices (random-regular and small-world graphs) in good agreement with previous results. However, our results for the quasi-two-dimensional graphs implemented in the D-Wave annealers (Chimera, Zephyr, and Pegasus) indicate only a zero-temperature spin-glass state, as their pseudo-critical temperature drifts towards smaller values. This implies that the asymptotic runtime to find the low-energy configuration of those graphs is likely to be polynomial in system size, nevertheless, this scaling may only be reached for very large system sizes -- much larger than existing annealers -- as we observe an abrupt increase in the computational cost of the simulations around the pseudo-critical temperatures. Thus, two-dimensional systems with local crossings can display enough complexity to make unfeasible the search with classical methods of low-energy configurations.